結果

問題 No.541 3 x N グリッド上のサイクルの個数
ユーザー koba-e964koba-e964
提出日時 2022-01-01 22:42:16
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 810 ms / 2,000 ms
コード長 6,488 bytes
コンパイル時間 13,336 ms
コンパイル使用メモリ 386,340 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-10 16:27:36
合計ジャッジ時間 40,082 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 36 ms
6,820 KB
testcase_01 AC 36 ms
6,820 KB
testcase_02 AC 44 ms
6,820 KB
testcase_03 AC 44 ms
6,816 KB
testcase_04 AC 52 ms
6,816 KB
testcase_05 AC 44 ms
6,816 KB
testcase_06 AC 52 ms
6,816 KB
testcase_07 AC 52 ms
6,820 KB
testcase_08 AC 59 ms
6,820 KB
testcase_09 AC 359 ms
6,816 KB
testcase_10 AC 367 ms
6,816 KB
testcase_11 AC 359 ms
6,816 KB
testcase_12 AC 362 ms
6,820 KB
testcase_13 AC 363 ms
6,820 KB
testcase_14 AC 377 ms
6,820 KB
testcase_15 AC 360 ms
6,816 KB
testcase_16 AC 370 ms
6,820 KB
testcase_17 AC 366 ms
6,816 KB
testcase_18 AC 375 ms
6,816 KB
testcase_19 AC 684 ms
6,816 KB
testcase_20 AC 679 ms
6,816 KB
testcase_21 AC 671 ms
6,816 KB
testcase_22 AC 807 ms
6,816 KB
testcase_23 AC 803 ms
6,816 KB
testcase_24 AC 799 ms
6,816 KB
testcase_25 AC 792 ms
6,816 KB
testcase_26 AC 793 ms
6,820 KB
testcase_27 AC 783 ms
6,816 KB
testcase_28 AC 786 ms
6,820 KB
testcase_29 AC 53 ms
6,816 KB
testcase_30 AC 60 ms
6,820 KB
testcase_31 AC 60 ms
6,816 KB
testcase_32 AC 69 ms
6,816 KB
testcase_33 AC 53 ms
6,816 KB
testcase_34 AC 61 ms
6,816 KB
testcase_35 AC 61 ms
6,816 KB
testcase_36 AC 70 ms
6,820 KB
testcase_37 AC 62 ms
6,820 KB
testcase_38 AC 68 ms
6,820 KB
testcase_39 AC 68 ms
6,816 KB
testcase_40 AC 363 ms
6,820 KB
testcase_41 AC 376 ms
6,820 KB
testcase_42 AC 367 ms
6,816 KB
testcase_43 AC 376 ms
6,816 KB
testcase_44 AC 348 ms
6,820 KB
testcase_45 AC 368 ms
6,820 KB
testcase_46 AC 360 ms
6,820 KB
testcase_47 AC 363 ms
6,820 KB
testcase_48 AC 368 ms
6,816 KB
testcase_49 AC 378 ms
6,820 KB
testcase_50 AC 374 ms
6,816 KB
testcase_51 AC 779 ms
6,820 KB
testcase_52 AC 810 ms
6,816 KB
testcase_53 AC 794 ms
6,820 KB
testcase_54 AC 777 ms
6,820 KB
testcase_55 AC 780 ms
6,816 KB
testcase_56 AC 781 ms
6,820 KB
testcase_57 AC 786 ms
6,816 KB
testcase_58 AC 777 ms
6,816 KB
testcase_59 AC 775 ms
6,820 KB
testcase_60 AC 799 ms
6,816 KB
testcase_61 AC 784 ms
6,816 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

// Registry.
#[derive(Clone, Default, Debug)]
struct Reg<T> {
    a: Vec<T>,
    inv: std::collections::HashMap<T, usize>,
}

impl<T: Default> Reg<T> {
    pub fn new() -> Self {
        Self::default()
    }
}

impl<T: std::hash::Hash + Eq + Clone> Reg<T> {
    pub fn get(&mut self, t: &T) -> usize {
        if !self.inv.contains_key(t) {
            let idx = self.a.len();
            self.a.push(t.clone());
            self.inv.insert(t.clone(), idx);
        }
        self.inv[t]
    }
    // init must have distinct elements.
    pub fn init<F>(&mut self, init: &[T], f: F) -> Vec<Vec<i64>>
    where F: Fn(T) -> Vec<T> {
        let mut que = std::collections::VecDeque::new();
        for t in init {
            let idx = self.get(t);
            que.push_back(idx);
        }
        let mut n = self.a.len();
        let mut vis = vec![false; n];
        let mut to = vec![vec![]; n];
        while let Some(v) = que.pop_front() {
            if vis[v] { continue; }
            let ans = f(self.a[v].clone());
            let mut entries = vec![];
            for elem in ans {
                let idx = self.get(&elem);
                entries.push(idx);
                if n <= idx {
                    // A newly created entry.
                    n = self.a.len();
                    vis.resize(n, false);
                    to.resize(n, vec![]);
                    que.push_back(idx);
                }
            }
            vis[v] = true;
            to[v] = entries;
        }
        let mut ans = vec![vec![0; n]; n];
        for i in 0..n {
            for &e in &to[i] {
                ans[i][e] += 1;
            }
        }
        ans
    }
}

#[derive(Clone, Default, Debug, Hash, Eq, PartialEq)]
struct State {
    back: i32,
    me: i32,
    uf: Vec<usize>,
    conn: i32,
}

// For each component, the root is always the maximum element.
fn uf_naive(uf: &mut [usize], x: usize, y: usize) {
    if uf[x] == uf[y] { return; }
    let n = uf.len();
    let r = max(uf[x], uf[y]);
    let other = r ^ uf[x] ^ uf[y];
    for i in 0..n {
        if uf[i] == other {
            uf[i] = r;
        }
    }
}

fn next(s: State) -> Vec<State> {
    let mut ans = vec![];
    for i in 0..16 {
        let back = i;
        for j in 0..8 {
            let me = j;
            // Find the degree of each vertex
            let mut pre = [0; 4];
            let mut now = [0; 4];
            for k in 0..3 {
                if (me & 1 << k) != 0 {
                    now[k] += 1;
                    now[k + 1] += 1;
                }
                if (s.me & 1 << k) != 0 {
                    pre[k] += 1;
                    pre[k + 1] += 1;
                }
            }
            for k in 0..4 {
                if (back & 1 << k) != 0 {
                    now[k] += 1;
                    pre[k] += 1;
                }
                if (s.back & 1 << k) != 0 {
                    pre[k] += 1;
                }
            }
            if pre.iter().any(|&x| x != 0 && x != 2) {
                continue;
            }
            // Connectedness
            let mut nuf = vec![0; 8];
            for k in 0..4 {
                nuf[k] = s.uf[k];
                nuf[k + 4] = k + 4;
            }
            for k in 0..4 {
                if (back & 1 << k) == 0 { continue; }
                // union-find
                uf_naive(&mut nuf, k, k + 4);
            }
            for k in 0..3 {
                if (me & 1 << k) == 0 { continue; }
                // union-find
                uf_naive(&mut nuf, k + 4, k + 5);
            }
            let mut uf = vec![0; 4];
            let mut conn = s.conn;
            for k in 0..4 {
                if pre[k] == 2 && nuf[k] == k {
                    conn += 1;
                }
                uf[k] = nuf[k + 4] - 4;
            }
            if conn <= 1 {
                ans.push(State {
                    back,
                    me,
                    uf,
                    conn,
                });
            }
        }
    }
    ans
}

fn squmul(a: &[Vec<i64>], b: &[Vec<i64>], mo: i64) -> Vec<Vec<i64>> {
    let n = a.len();
    let mut ret = vec![vec![0; n]; n];
    for i in 0..n {
        for j in 0..n {
            for k in 0..n {
                ret[i][k] += a[i][j] * b[j][k];
                ret[i][k] %= mo;
            }
        }
    }
    ret
}

fn squpow(a: &[Vec<i64>], mut e: i64, mo: i64) -> Vec<Vec<i64>> {
    let n = a.len();
    let mut sum = vec![vec![0; n]; n];
    for i in 0..n { sum[i][i] = 1; }
    let mut cur = a.to_vec();
    while e > 0 {
        if e % 2 == 1 {
            sum = squmul(&sum, &cur, mo);
        }
        cur = squmul(&cur, &cur, mo);
        e /= 2;
    }
    sum
}

fn solve() {
    let n: i64 = get();
    let mut reg = Reg::<State>::new();
    let mut uf = vec![0; 4];
    for i in 0..4 {
        uf[i] = i;
    }
    let init = State { back: 0, me: 0, uf: uf.clone(), conn: 0 };
    let term = State { back: 0, me: 0, uf: uf.clone(), conn: 1 };
    let tmp = next(init.clone());
    for j in 0..8 {
        eprintln!("j = {}", j);
        let tmp = next(tmp[j].clone());
        for t in tmp {
            eprintln!("{:?}", t);
        }
        eprintln!();
    }
    let mat = reg.init(&[init.clone()], next);
    eprintln!("M: {} * {}", reg.a.len(), reg.a.len());
    let idx1 = reg.get(&init);
    let idx2 = reg.get(&term);
    let pw = squpow(&mat, n + 2, 1_000_000_007);
    println!("{}", pw[idx1][idx2]);
}

fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}
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